Horses playground

The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m2, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?

Result

x =  430 m

Solution:

S=400 m2 a=31 m c=19 m n=5  S=a+c2 d  d=2 Sa+c=2 40031+19=16 m  b=d2+(ac)2=162+(3119)2=20 m  o=a+b+c+d=31+20+19+16=86 m  x=n o=5 86=430 mS=400 \ \text{m}^2 \ \\ a=31 \ \text{m} \ \\ c=19 \ \text{m} \ \\ n=5 \ \\ \ \\ S=\dfrac{ a+c }{ 2 } \cdot \ d \ \\ \ \\ d=\dfrac{ 2 \cdot \ S }{ a+c }=\dfrac{ 2 \cdot \ 400 }{ 31+19 }=16 \ \text{m} \ \\ \ \\ b=\sqrt{ d^2 + (a-c)^2 }=\sqrt{ 16^2 + (31-19)^2 }=20 \ \text{m} \ \\ \ \\ o=a+b+c+d=31+20+19+16=86 \ \text{m} \ \\ \ \\ x=n \cdot \ o=5 \cdot \ 86=430 \ \text{m}



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